I would warn against going too short. At times I didn't like my name (my real name: not Emily), because its so short with my one syllable last name. I love my name in general but at times I wished it was longer. I even made up alternative spellings. At least I have a longer middle name to add some balance.

Clara is such a wonderful name, but I see your issue. I also love Hazel, although I can predict this one getting quite big. I know a few young Hazels all born within the last year... I'd steer clear of 1 syllable first names with your 1 syllable surname.